Question

Find the interval in which f(x) = 3x2 - 2x is decreasing.

Answer 1

Option (3)

Explanation:

Given function is,

f(x) = 3x² - 2x

=
`3(x^(2) -(2)/(3)x)`

=
`3(x^(2) -(2)/(3)x+(1)/(9)-(1)/(9))`

=
`3(x^(2)-(2)/(3)x+(1)/(9))-(1)/(3)`

=
`3(x-(1)/(3))^2-(1)/(3)`

Vertex of the parabola →
`((1)/(3),-(1)/(3))`

Here, leading coefficient is positive (+3),

Therefore, parabola will open upwards.

In a parabola opening upwards function decreases from negative infinity to the x value of the vertex.

Function will decrease in the interval (-∞,
`(1)/(3)`).

Option (3) will be the answer.